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.bold.center[Having access to the gradients can make the fit orders of magnitude faster than finite difference]
---
-# Enable new techniques with autodiff
-
-.kol-2-3[
-* Familiar (toy) example: Optimizing selection "cut" for an analysis.
-Place discriminate selection cut on observable $x$ to maximize significance.
-* Traditionally, step along values in $x$ and calculate significance at each selection. Keep maximum.
-* Need differentiable analogue to non-differentiable "cut".
-Weight events using activation function of sigmoid
-
-.center[$w=\left(1 + e^{-\alpha(x-c)}\right)^{-1}$]
-
-* Most importantly though, with the differentiable model we have access to the gradient $\partial_{x} f(x)$
-* So can find the maximum significance at the point where the gradient of the significance is zero $\partial_{x} f(x) = 0$
-* With a simple gradient descent algorithm can easily automate the significance optimization
+# Enabling new tools with autodiff [TODO: CLARIFY]
+.kol-1-1[
+.kol-1-3[
+
+ +
] -.kol-1-3.center[ +.kol-1-3[ ++ +
+] +.kol-1-3[- - - +
] +] + +.kol-1-3[ +* Counting experiment for presence of signal process +* Place discriminate selection cut on observable $x$ to maximize significance $f(x)$ +* Step along cut values in $x$ and calculate significance +] +.kol-1-3[ +* Need differentiable analogue to non-differentiable cut +* Weight events using activation function of sigmoid + +.center[$w=\left(1 + e^{-\alpha(x-c)}\right)^{-1}$] +] +.kol-1-3[ +* With a simple gradient descent algorithm can easily automate the significance optimization +* Allows for the "cut" to become a parameter that can be differentiated through for the larger analysis +] --- # New Art: Analysis as a Differentiable Program